MLS also announced plans to have a new club in Austin, Texas, run by Anthony Precourt, the current Crew owner who will relocate his franchise rights as he had planned to do with the Crew after this season.
That would delay the start of a team in the Texas capital until 2021 at the latest, but Austin would be set as the 27th MLS team, the penultimate squad in the league's expansion plan.
For the Crew, adding Haslam to local investor Pete Edwards could produce the funding for a new stadium and a long-term plan to keep one of the original MLS teams in its home city.
"We value and appreciate the benefits a professional sports franchise can bring to a community and are hopeful to be part of the solution to keep the Crew in Columbus," the Haslam family said in a statement.
Although the deal is not complete, "significant progress" has been made, an MLS statement said.
"For the club to be successful in Columbus, it requires strong local partners, long-term corporate support, a strong season ticket base and long-term plans for a stadium, practice facilities and associated sites," MLS said.
"MLS is committed to keeping Crew SC in Columbus should we continue to make progress on these critical components and agree to key terms with the investor group."
The league also remains "very committed to (Precourt's) plan to launch an MLS club in Austin and is excited for Austin to become a great addition to MLS.
"Regardless of any scenario in Columbus, there is a clear path forward for Precourt Sports Ventures to operate Austin FC as a Major League Soccer club," the MLS statement said.
"While timing for Austin FC is still to be finalized, we are confident that the team will begin play no later than 2021."
MLS has 23 teams this season with plans to add clubs in Nashville, Cincinnati and Miami, where David Beckham's Inter Miami squad is finally expected to take the field in 2020 after years of struggles with stadium location issues.
The Columbus Partnership alliance between the Haslam and Edwards families said in a statement it was "optimistic about our recent conversations with MLS regarding the potential sale of the operating rights of the Columbus Crew.
"While there are many details to be worked out, our alliance is working diligently and collaboratively with the league to keep the Crew in its community."